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JEE Main 2022 28 Jul Evening shift Question Paper with Solutions | JEE Arc

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JEE Main 202228 Jul, Evening shift

Physics 22Chemistry 19Mathematics 29

Physics

Q52The distance of centre of mass from end A of a one dimensional rod (AB) having mass density ρ=ρ₀(1-(x²)/(L²)) kg / m and length L (in meter) is (3 L)/(α) m…Rotational Motion
Q55An electrical bulb rated 220 V, 100 W, is connected in series with another bulb rated 220 V, 60 W. If the voltage across combination is 220 V, the power…Current Electricity
Q59In an experiment with a convex lens, The plot of the image distance (v^()) against the object distance (.μ^()) measured from the focus gives a curve v^()…Optics
Q61At a certain temperature, the degrees of freedom per molecule for gas is 8. The gas performs 150 J of work when it expands under constant pressure. The amount…Thermodynamics
Q64A ball is thrown vertically upwards with a velocity of 19.6 ~ms⁻¹ from the top of a tower. The ball strikes the ground after 6 ~s. The height from the ground…Kinematics
Q65A string of area of cross-section 4 ~mm² and length 0.5 ~m is connected with a rigid body of mass 2 ~kg. The body is rotated in a vertical circular path of…Properties of Solids and Liquids
Q68The potential energy of a particle of mass 4 ~kg in motion along the x-axis is given by U=4(1- cos 4 x) J. The time period of the particle for small…Oscillations and Waves
Q70In an experiment to find acceleration due to gravity (g) using simple pendulum, time period of 0.5 ~s is measured from time of 100 oscillation with a watch of…Units and Measurements
Q5942A transformer operating at primary voltage 8 kV and secondary voltage 160 ~V serves a load of 80 ~kW. Assuming the transformer to be ideal with purely…Electromagnetic Induction and Alternating Currents
Q6125A radioactive sample decays 7/8 times its original quantity in 15 minutes. The half-life of the sample isAtoms and Nuclei
Q6160A slab of dielectric constant K has the same cross-sectional area as the plates of a parallel plate capacitor and thickness 3/4 ~d, where d is the separation…Electrostatics
Q6366A FM Broadcast transmitter, using modulating signal of frequency 20 kHz has a deviation ratio of 10. The Bandwidth required for transmission is:Communication Systems
Q6436Given below are two statements: Statement I: A uniform wire of resistance 80 Ω is cut into four equal parts. These parts are now connected in parallel. The…Current Electricity
Q6652Two streams of photons, possessing energies equal to five and ten times the work function of metal are incident on the metal surface successively. The ratio…Dual Nature of Matter and Radiation
Q6801Sun light falls normally on a surface of area 36 ~cm² and exerts an average force of 7.2 × 10⁻⁹ ~N within a time period of 20 minutes. Considering a case of…Electromagnetic Waves
Q7050The power of a lens (biconvex) is 1.25 ~m⁻¹ in particular medium. Refractive index of the lens is 1.5 and radii of curvature are 20 ~cm and 40 ~cm…Optics
Q7407A vessel contains 14 ~g of nitrogen gas at a temperature of 27^(°) C. The amount of heat to be transferred to the gas to double the r.m.s speed of its…Kinetic Theory of Gases
Q7690The magnetic field at the center of current carrying circular loop is B₁. The magnetic field at a distance of √(3) times radius of the given circular loop…Magnetic Effects of Current and Magnetism
Q7822At time t=0 a particle starts travelling from a height 7 z ~cm in a plane keeping z coordinate constant. At any instant of time it's position along the x and…Kinematics
Q7995A pressure-pump has a horizontal tube of cross sectional area 10 ~cm² for the outflow of water at a speed of 20 ~m / s. The force exerted on the vertical wall…Properties of Solids and Liquids
Q8210Assume there are two identical simple pendulum clocks. Clock - 1 is placed on the earth and Clock - 2 is placed on a space station located at a height h above…Oscillations and Waves
Q8262Consider the efficiency of carnot's engine is given by η=(α β)/(sin θ) log e (β x)/(k T), where α and β are constants. If T is temperature, k is Boltzmann…Units and Measurements

Chemistry

Q3At 600 ~K, 2 ~mol of NO are mixed with 1 ~mol of O₂. 2 NO (g) +O₂(g) 2 NO₂(g) The reaction occurring as above comes to equilibrium under a total pressure of 1…Equilibrium
Q7On reaction with stronger oxidizing agent like KIO₄, hydrogen peroxide oxidizes with the evolution of O₂. The oxidation number of I in KIO₄ changes to _ _ _ _…Hydrogen
Q10A sample of 0.125 ~g of an organic compound when analyzed by Duma's method yields 22.78 ~mL of nitrogen gas collected over KOH solution at 280 ~K and 759 ~mm…Principles Related to Practical Chemistry
Q13Metal M crystallizes into a fcc lattice with the edge length of 4.0 × 10⁻⁸ ~cm. The atomic mass of the metal is _ _ _ _ _ _ g / mol. (Nearest integer) (. Use…Solid State
Q14A gaseous mixture of two substances A and B, under a total pressure of 0.8 atm is in equilibrium with an ideal liquid solution. The mole fraction of substance…Solutions
Q152L of 0.2M H₂SO₄ is reacted with 2L of 0.1M NaOH solution, the molarity of the resulting product Na₂SO₄ in the solution is _ _ _ _ m illimolar. (Nearest…Some Basic Concepts in Chemistry
Q16If the wavelength for an electron emitted from H -atom is 3.3 × 10⁻¹⁰ ~m, then energy absorbed by the electron in its ground state compared to minimum energy…Atomic Structure
Q19Among the following the number of state variables is _ _ _ _ _ _ _. Internal energy (U) Volume (V) Heat (q) Enthalpy (H)Chemical Thermodynamics
Q84Arrange the following in increasing order of reactivity towards nitration A. p-xylene B. bromobenzene C. mesitylene D. nitrobenzene E. benzene Choose the…Some Basic Principles of Organic Chemistry
Q136Given below are two statements: One is labelled as Assertion A and the other is labelled as Reason R Assertion A: Thin layer chromatography is an adsorption…Some Basic Principles of Organic Chemistry
Q542Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R Assertion A: Aniline on nitration yields ortho, meta para…Organic Compounds Containing Nitrogen
Q742Match List I with List II List - I (Complex) List - II (Hybridization) (A) Ni (CO)₄ (I) s p³ (B) [Ni (CN)₄ ]²⁻ (II) s p³ d² (C) [Co (CN)₆ ]³⁻ (III) d²s p³ (D)…Coordination Compounds
Q1203The products obtained during treatment of hard water using Clark's method are:Hydrogen
Q1288Given below are two statements: One is labelled as Assertion A and the other is labelled as Reason R Assertion A: Permanganate titrations are not performed in…Equilibrium
Q1495Dinitrogen and dioxygen, the main constituents of air do not react with each other in atmosphere to form oxides of nitrogen because:p-Block Elements
Q1894The correct decreasing order for metallic character is:S Block Elements
Q1895Statement I: An alloy of lithium and magnesium is used to make aircraft plates. Statement II: The magnesium ions are important for cell-membrane integrity. In…S Block Elements
Q2208Given below are two statements: One is labelled as Assertion A and the other is labelled as Reason R Assertion A: Zero orbital overlap is an out of phase…Atomic Structure
Q2307Given below are two statements: One is labelled as Assertion A and the other is labelled as Reason R Assertion A: The reduction of a metal oxide is easier if…Chemical Thermodynamics

Mathematics

Q24Let the coefficients of the middle terms in the expansion of (1/(√(6))+β x)⁴,(1-3 β x)² and (1-(β)/2 x)⁶, β>0, respectively form the first three terms of an…Binomial Theorem and Its Simple Applications
Q25If 1 + (2 + ⁴⁹C₁ + ⁴⁹C₂ +... + ⁴⁹C₄₉)(⁵⁰C₂ + ⁵⁰C₄ +... + ⁵⁰C₅₀) is equal to 2ⁿ · m, where m is odd, then n+m is equal to _ _ _ _ _.Binomial Theorem and Its Simple Applications
Q27Let z=a+i b, b ≠ 0 be complex numbers satisfying z²=z · 2^(1-z). Then the least value of n N, such that zⁿ=(z+1)ⁿ, is equal to _ _ _ _ _.Complex Numbers and Quadratic Equations
Q29The value of the integral ∫₀^((π)/2) 60 (sin (6 x))/(sin x) d x is equal to _ _ _ _ _.Integral Calculus
Q33Let the tangents at the points P and Q on the ellipse (x²)/2+(y²)/4=1 meet at the point R(√(2), 2 √(2)-2). If S is the focus of the ellipse on its negative…Coordinate Geometry
Q41Two tangent lines l₁ and l₂ are drawn from the point (2,0) to the parabola 2 y²=-x. If the lines l₁ and l₂ are also tangent to the circle (x-5)²+y²=r, then…Coordinate Geometry
Q42A class contains b boys and g girls. If the number of ways of selecting 3 boys and 2 girls from the class is 168, then b+3 ~g is equal to _ _ _ _ _ _.Permutations and Combinations
Q44A bag contains 4 white and 6 black balls. Three balls are drawn at random from the bag. Let X be the number of white balls, among the drawn balls. If σ² is…Statistics and Probability
Q476/(3¹²) + 10/(3¹¹) + 20/(3¹⁰) + 40/(3⁹) +... + 10240/3 = 2ⁿ. m, where m is odd, then m. n is equal to _ _ _ _ _ _.Sequence and Series
Q2451Let the lines (x-1)/(λ)=(y-2)/1=(z-3)/2 and (x+26)/(-2)=(y+18)/3=(z+28)/(λ) be coplanar and P be the plane containing these two lines. Then which of the…Three Dimensional Geometry
Q2599A plane P is parallel to two lines whose direction ratios are -2,1,-3 and -1,2,-2 and it contains the point (2,2,-2). Let P intersect the co-ordinate axes at…Three Dimensional Geometry
Q2727The function f(x)=x e^(x(1-x)), x R, is:Limit, Continuity and Differentiability
Q2850The area enclosed by the curves y= log e (x+e²), x= log e (2/y) and x= log e 2, above the line y=1 is:Integral Calculus
Q3138Let the tangents at two points A and B on the circle x²+y²-4 x+3=0 meet at origin O(0,0). Then the area of the triangle OAB is:Coordinate Geometry
Q3444Let I n (x)=∫₀ˣ 1/((t²+5)ⁿ) d t, n=1,2,3,. Then:Integral Calculus
Q3501The differential equation of the family of circles passing through the points (0,2) and (0,-2) is:Differential Equations
Q3550Let y=y(x) be the solution curve of the differential equation (d y)/(d x)+1/(x²-1) y=((x-1)/(x+1))^(1 / 2), x >1 passing through the point (2, √(1/3)). Then…Differential Equations
Q3696Let x(t)=2 √(2) cos t √(sin 2 t) and y(t)=2 √(2) sin t √(sin 2 t), t (0, (π)/2). Then (1+((d y)/(d x))²)/((d² y)/(d x²)) at t=(π)/4 is equal to:Limit, Continuity and Differentiability
Q3870Let f(x)=a x²+b x+c be such that f(1)=3, f(-2)=λ and f(3)=4. If f(0)+f(1)+f(-2)+f(3)=14, then λ is equal to:Sets, Relations and Functions
Q3933A horizontal park is in the shape of a triangle OAB with AB=16. A vertical lamp post OP is erected at the point O such that PAO= PBO=15^(°) and PCO=45^(°)…Height and Distance
Q3976Let the hyperbola H: (x²)/(a²)-(y²)/(b²)=1 pass through the point (2 √(2),-2 √(2)). A parabola is drawn whose focus is same as the focus of H with positive…Coordinate Geometry
Q4113The sum of the absolute maximum and absolute minimum values of the function f(x)= tan ⁻¹(sin x- cos x) in the interval [0, π] is:Trigonometry
Q4157The function f: R → R defined by f(x)= lim n → ∞ (cos (2 π x)-x²ⁿ sin (x-1))/(1+x²ⁿ⁺¹-x²ⁿ) is continuous for all x in:Limit, Continuity and Differentiability
Q4421Let p: Ramesh listens to music. q: Ramesh is out of his village. r: It is Sunday. s: It is Saturday. Then the statement "Ramesh listens to music only if he is…Mathematical Reasoning
Q4648Let A and B be any two 3 × 3 symmetric and skew symmetric matrices respectively. Then which of the following is NOT true?Matrices and Determinants
Q4965Let A and B be two events such that P(B A)=2/5, P(A B)=1/7 and P(A B)=1/9 · Consider (S1) P(A^() B)=5/6, (S2) P(A^() B^())=1/18 Then:Statistics and Probability
Q5086Let S= [-6,3]-\-2,2 (|x+3|-1)/(|x|-2) ≥ 0 and T= Z: x²-7|x|+9 ≤ 0. Then the number of elements in S T is:Complex Numbers and Quadratic Equations
Q5158Let α, β be the roots of the equation x²-√(2) x+√(6)=0 and 1/(α²)+1, 1/(β²)+1 be the roots of the equation x²+a x+b=0. Then the roots of the equation…Complex Numbers and Quadratic Equations
Q5778Let S be the set of all a R for which the angle between the vectors u=a(log e b) i-6 j+3 k and v=(log e b) i+2 j+2 a(log e b) k, (b>1) is acute. Then S is…Vector Algebra